Average Error: 2.8 → 2.9
Time: 10.4s
Precision: 64
\[\frac{x}{y - z \cdot t}\]
↓
\[x \cdot \frac{1}{y - z \cdot t}\]
\frac{x}{y - z \cdot t}
↓
x \cdot \frac{1}{y - z \cdot t}
double f(double x, double y, double z, double t) {
        double r357013 = x;
        double r357014 = y;
        double r357015 = z;
        double r357016 = t;
        double r357017 = r357015 * r357016;
        double r357018 = r357014 - r357017;
        double r357019 = r357013 / r357018;
        return r357019;
}
↓
double f(double x, double y, double z, double t) {
        double r357020 = x;
        double r357021 = 1.0;
        double r357022 = y;
        double r357023 = z;
        double r357024 = t;
        double r357025 = r357023 * r357024;
        double r357026 = r357022 - r357025;
        double r357027 = r357021 / r357026;
        double r357028 = r357020 * r357027;
        return r357028;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.8
Target1.9
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x \lt 2.13783064348764444 \cdot 10^{131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array}\]

Derivation

  1. Initial program 2.8

    \[\frac{x}{y - z \cdot t}\]
  2. Using strategy rm

  3. Applied div-inv2.9

    \[\leadsto \color{blue}{x \cdot \frac{1}{y - z \cdot t}}\]

  4. Final simplification2.9

    \[\leadsto x \cdot \frac{1}{y - z \cdot t}\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t)))))

  (/ x (- y (* z t))))